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Real World Applications of Linear Equations Yes, there really are uses for them!! Math 208 ~ College Mathematics I Objective: Apply the concepts of slope and intercept to real-life situations Today’s Objectives To define the slope of a linear equation a real world context To find a meaning for an equation’s x & y-intercepts Brief Review of Graphing Solve the equation for y 2x + y = 3 y = – 2x + 3 Make a table and find x y = –2x + 3 y –1 some ordered pair y=2+3 5 0 Y=0+3 3 values 1 Y = –2 + 3 1 2 Y = –4 + 3 –1 Graph the Equation Graph the ordered pairs (-1, 5) Draw the line (0, 3) (1, 1) (shows all the (2, -1) possible solutions) First Problem to follow along. Use the handout What do we know? A pillow company buys ribbon in 100 foot rolls. 2.5 feet of ribbon are needed to decorate each pillow. What do we need to do? Write an equation. Use y for the amount ribbon left on the roll and x for the number of pillows made. Fill in the table and draw the a graph. Write Equation & Fill in the Table # Pillows # of Feet of Ribbon Made y = 100 – 2.5x Remaining on Roll 0 100 – 0 100 1 100 – 2.5 97.5 2 100 – 5 95 3 100 – 7.5 92.5 4 100 – 10 90 Draw the graph 100 90 80 70 60 50 40 30 20 10 1 2 3 4 5 6 7 8 9 10 Questions for 100 90 80 Discussion 70 60 50 40 30 y = 100 – 2.5x 20 1. What is the slope? 10 1 2 3 4 5 6 7 8 9 10 What does it represent? 2. Why is the slope negative? 3. What is the y-intercept? What does it represent? 4. What is the x-intercept? What does it represent? Second Problem What do we know? A swimming pool holds 450 gallons of water. The pool currently contains 100 gallons of water. A hose deposits 50 gallons of water in the pool each minute. What do we need to do? Write an equation. Use y for the amount of water in the pool and x for the number of minutes the hose runs. Fill in the table and graph the information. Fill in the Table # of Minutes Hose # of Liters in is in Pool y = 100 + 50x The Pool 0 100 + 0 100 1 100 + 50 150 2 100 + 100 200 3 100 + 150 250 4 100 + 200 300 Draw the Graph 500 450 400 350 300 250 200 150 100 50 1 2 3 4 5 6 7 8 9 10 500 450 Questions for 400 350 Discussion 300 250 200 150 y = 100 + 50x 100 1. What is the slope? 50 1 2 3 4 5 6 7 8 9 10 2. What does it represent? 3. What is the y-intercept? What does it represent? 4. Why does this graph contain a line segment (have an end)? Conclusions What kinds of real life applications are linear? (What do these situations have in common?) They both have a Constant Rate of Change (SLOPE) What does the slope represent? The slope represents the rate of change What does the y=intercept represent? The y-intercept represents the y value before the rate begins. x = 0